Although the representation theory of Yangians is quite developed, some elementary questions have remained unanswered. We answer some of them in a joint paper with Y. Billig and V. Futorny by giving an irreducibility criterion for the Verma modules over the Yangians. Like for representations of the simple Lie algebras, every Verma module over a Yangian has a unique irreducible quotient. We also give necessary and sufficient conditions for the weight spaces of this quotient to be finite-dimensional. In the A type, these conditions were found independently by Brundan and Kleshchev.


	School of Mathematics and Statistics Algebra Seminar